US10255393B2 - Optimally placing photovoltaic arrays to maximize value of energy production based on peak power production, local solar radiation, weather, electricity market prices and rate structures - Google Patents
Optimally placing photovoltaic arrays to maximize value of energy production based on peak power production, local solar radiation, weather, electricity market prices and rate structures Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02S—GENERATION OF ELECTRIC POWER BY CONVERSION OF INFRARED RADIATION, VISIBLE LIGHT OR ULTRAVIOLET LIGHT, e.g. USING PHOTOVOLTAIC [PV] MODULES
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F24—HEATING; RANGES; VENTILATING
- F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
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- Y02B10/20—Solar thermal
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/50—Photovoltaic [PV] energy
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Definitions
- the present invention relates generally to the photovoltaic systems, and more particularly to optimally placing photovoltaic arrays to maximize the value of energy production based on peak power production, local solar radiation, weather, electricity market prices and rate structures.
- PV system is an arrangement of components designed to supply usable electric power for a variety of purposes, using the sun (or, less commonly, other light sources) as the power source.
- PV systems may be built in various configurations: off-grid without battery (array-direct); off-grid with battery storage for DC-only appliances; off-grid with battery storage for AC and DC appliances; grid-tie without battery; and grid-tie with battery storage.
- a photovoltaic array (also called a solar array) consists of multiple photovoltaic modules, casually referred to as solar panels, to convert solar radiation (sunlight) into usable direct current (DC) electricity.
- a photovoltaic system for residential, commercial, or industrial energy supply normally contains an array of photovoltaic (PV) modules, one or more DC to alternating current (AC) power converters (also known as inverters), a racking system that supports the solar modules, electrical wiring and interconnections, and mounting for other components.
- PV photovoltaic
- AC alternating current
- a photovoltaic system may include any or all of the following: a revenue-grade meter, a maximum power point tracker (MPPT), a battery system and charger, a global positioning system (GPS) solar tracker, energy management software, solar concentrators, solar irradiance sensors, an anemometer, or task-specific accessories designed to meet specialized requirements for a system owner.
- MPPT maximum power point tracker
- GPS global positioning system
- the number of modules in the system and the modules' rated capacity determines the total DC watts capable of being generated by the solar array; however, the inverter ultimately governs the amount of AC watts that can be distributed for consumption.
- solar PV panels are often installed on roofs and are typically set tilted and arranged in spaced-apart rows. For flat roofs, there is more flexibility for how to place the arrays.
- There have been many investigations into the optimal tilt for solar PV system to maximize the energy production i.e., maximize the conversion of solar radiation (sunlight) into usable direct current (DC) electricity).
- Many of these analyses consider solar energy production assuming that a southern azimuth (in the northern hemisphere) is optimal for energy production.
- PV orientation Another consideration for optimal PV orientation is the value of the electricity generated. Because solar energy production does not always precisely align with maximum electricity grid load or price, even placements that might be non-optimal from an energy production basis might be optimal on an economic or peak power production basis. For example, one analysis used day-ahead market electricity prices to determine optimal solar PV orientations in California. The conclusion of such an analysis was that the market electricity prices shifted the optimal orientation of some arrays west of south.
- FIG. 1 illustrates a hardware configuration of a computer system which is representative of a hardware environment for practicing the present invention
- FIG. 2 is a flowchart of a method for maximizing the value of energy production based on multiple inputs, offsetting building peak power consumption, local solar radiation, weather, geography, electricity market prices and rate structures in accordance with an embodiment of the present invention
- FIG. 3 is a table (Table 1) that summarizes the results of the various cases for both total energy production and the value of the energy produced in Austin, Tex. in accordance with an embodiment of the present invention
- FIG. 4 shows the total number of kWh per year produced (normalized for 1 m 2 of array) for every combination of azimuth and tilt, 90°-270° and 0°-45°, respectfully using clear-sky radiation and typical meteorological year (TMY) weather data in accordance with an embodiment of the present invention
- FIG. 5 shows the total number of kWh per year produced (normalized for 1 m 2 of array) for every combination of azimuth and tilt, 90°-270° and 0°-45°, respectively, using TMY radiation and weather on optimal placement in accordance with an embodiment of the present invention
- FIG. 6 is a heat map of model results for measured 2012-2013 radiation and weather with coincident Electric Reliability Council of Texas (ERCOT) wholesale electricity prices showing an optimal value ($/m 2 /year) azimuth of 204° and 25° tilt for Austin, Tex. in accordance with an embodiment of the present invention
- FIG. 7 is a heat map of model results for TMY radiation and weather with average ERCOT wholesale electricity prices showing an optimal value ($/m 2 /year) azimuth of 219° and 29° tilt for Austin, Tex. in accordance with an embodiment of the present invention
- FIG. 8 shows the values associated with Austin TMY solar radiation and weather with Austin Energy's residential Time-of-Use (TOU) rate and also shows how azimuth and tilt are related under the TOU rate in accordance with an embodiment of the present invention
- FIG. 9 shows the values associated with Austin TMY solar radiation and weather with ERCOT prices from 2011 in accordance with an embodiment of the present invention
- FIG. 10 is a map of continental U.S. showing the energetically optimal azimuth of solar PV systems in accordance with an embodiment of the present invention
- FIG. 11 is a map of continental U.S. showing the optimal azimuth of solar PV systems when considering the value of the solar energy produced using electric utility rates local to the solar arrays in accordance with an embodiment of the present invention
- FIG. 12 is a map of continental U.S. showing deviation from the rule of thumb tilt (local latitude) based on total energy production in accordance with an embodiment of the present invention
- FIG. 13 is a map of continental U.S. showing deviation from the rule of thumb tilt (local latitude) based on the value of local energy production using electric utility rates local to the solar arrays in accordance with an embodiment of the present invention
- FIGS. 14A-14B are plots that show the average generation curves for various solar placements in Austin using TMY data and average ERCOT wholesale electricity market prices, including optimal peak placement in accordance with an embodiment of the present invention.
- FIG. 15 is a table (Table 2) that summarizes the differences in energy produced (area under the curves, relative to the rule of thumb placement) from the placements shown in FIGS. 14A-14B in accordance with an embodiment of the present invention.
- FIG. 1 illustrates a hardware configuration of a computer system 100 which is representative of a hardware environment for practicing the present invention.
- Computer system 100 has a processor 101 coupled to various other components by system bus 102 .
- An operating system 103 runs on processor 101 and provides control and coordinates the functions of the various components of FIG. 1 .
- An application 104 in accordance with the principles of the present invention runs in conjunction with operating system 103 and provides calls to operating system 103 where the calls implement the various functions or services to be performed by application 104 .
- Application 104 may include, for example, a program for optimally placing photovoltaic arrays to maximize the value of energy production based on peak power production, local solar radiation, weather, electricity market prices and rate structures as discussed further below in association with FIGS. 2-15 .
- ROM 105 is coupled to system bus 102 and includes a basic input/output system (“BIOS”) that controls certain basic functions of computer system 100 .
- RAM random access memory
- disk adapter 107 are also coupled to system bus 102 .
- software components including operating system 103 and application 104 may be loaded into RAM 106 , which may be computer system's 100 main memory for execution.
- Disk adapter 107 may be an integrated drive electronics (“IDE”) adapter that communicates with a disk unit 108 , e.g., disk drive.
- IDE integrated drive electronics
- the program for optimally placing photovoltaic arrays to maximize the value of energy production based on peak power production, local solar radiation, weather, electricity market prices and rate structures may reside in disk unit 108 or in application 104 .
- Computer system 100 may further include a communications adapter 109 coupled to bus 102 .
- Communications adapter 109 interconnects bus 102 with an outside network thereby enabling computer system 100 to communicate with other such systems.
- I/O devices may also be connected to computer system 100 via a user interface adapter 110 and a display adapter 111 .
- Keyboard 112 , mouse 113 and speaker 114 may all be interconnected to bus 102 through user interface adapter 110 .
- a display monitor 115 may be connected to system bus 102 by display adapter 111 . In this manner, a user is capable of inputting to computer system 100 through keyboard 112 or mouse 113 and receiving output from computer system 100 via display 115 or speaker 114 .
- the present invention may be a system, a method, and/or a computer program product.
- the computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention.
- the computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device.
- the computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing.
- a non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing.
- RAM random access memory
- ROM read-only memory
- EPROM or Flash memory erasable programmable read-only memory
- SRAM static random access memory
- CD-ROM compact disc read-only memory
- DVD digital versatile disk
- memory stick a floppy disk
- a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon
- a computer readable storage medium is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.
- Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network.
- the network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers.
- a network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device.
- Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages.
- the computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server.
- the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).
- electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention.
- These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.
- These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks.
- the computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks.
- each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s).
- the functions noted in the block may occur out of the order noted in the figures.
- two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved.
- one analysis used day-ahead market electricity prices to determine optimal solar PV orientations in California. The conclusion of such an analysis was that the market electricity prices shifted the optimal orientation of some arrays further west of south. While there have been some analysis in determining the optimal tilt and azimuth angles as well as determining the optimal PV orientation based on the value of the electricity generated, there has been no analysis considering the production of AC electricity (after panel, inverter and other derate losses) as the metric for optimal placement. Furthermore, such analyses were limited to a local geographic area without considering multiple economic inputs. Additionally, such analyses did not consider the value of energy production from the perspective of various users (e.g., residential customers, utility companies, businesses), where the “value” may correspond to an economic value or a non-economic value (e.g., reduction in carbon dioxide).
- a non-economic value e.g., reduction in carbon dioxide
- the principles of the present invention provide a means for optimally placing photovoltaic arrays to maximize the value of energy production based on multiple inputs, including peak power production, local solar radiation, weather, electricity market prices and rate structures as discussed below in connection with FIGS. 2-15 .
- the value of maximizing energy production can correspond to maximizing or optimizing energy, power, economic value or non-economic value (e.g., carbon dioxide displacement).
- the value of maximizing energy production is dependent upon the user in question (e.g., resident in a residential area, a utility company, a business). That is, the value of maximizing energy production is dependent upon the user who is to benefit from the analysis discussed herein.
- FIG. 2 is a flowchart of a method 200 for maximizing the value of energy production based on multiple inputs, including peak power production, local solar radiation, weather, electricity market prices and rate structures in accordance with an embodiment of the present invention.
- the analysis of method 200 uses available solar insolation and electricity price data to: (1) determine the insolation on a given plane (with available solar radiation tools); (2) build a system-based solar PV production model; (3) estimate the total energy, power, and economic impacts of system azimuth and tilt (placement) for Austin, Tex.; (4) extend the analysis to other locations across the United States; and (5) explore the peak power production implications of varying solar placements using the aforementioned datasets.
- the principles of the present invention could also be used to deploy multiple arrays at different placements in order to mitigate the effects of all local solar arrays coming on or going off line at the same time, commonly referred to as “ramp rate.”
- the incident solar radiation for various placements of photovoltaic arrays accommodating different azimuths and tilts is calculated.
- the incident solar radiation for multiple azimuths and tilts were calculated so as to determine the value of various solar placements.
- Many models use the same methods for calculating the direct beam and reflected, but differ on methods of calculating incident diffuse from the sky.
- method 200 utilizes the solar package of the R language (O. Perpinan, “Solar Radiation and Photovoltaic Systems with R,” Journal of Statistical Software, Vol.
- Equation 3-5 I B is the beam radiation on the horizontal plane, R B is the ratio of beam radiation on the tilted plane to that on a horizontal surface given by Equations 3-5:
- ⁇ is the declination
- ⁇ is the local latitude
- ⁇ is the tilt of the surface
- ⁇ is the surface azimuth angle
- ⁇ is the hour angle
- RT,I is the reflected radiation on the tilted plane given by Equation 6:
- Equation 7 The diffuse component D T from Hay and McKay with the horizon brightness correction proposed by Reindl et al. is given by Equation 7:
- D 0 is the diffuse radiation on the horizontal plane
- Equations (1)-(7) are a commonly used model that the principles of the present invention may use other models for estimating the solar radiation on a tilted plane.
- step 202 the alternating-current (AC) solar photovoltaic electricity energy (kilowatts/hour) and power (kilowatts) production is estimated from the calculated solar radiation on a plane (calculated in step 201 ), weather data and geographic data (e.g., shadows from mountains).
- AC solar PV electricity production from solar radiation on a plane a solar PV energy production model was built. The overall model is given in Equations 8-9:
- the efficiency of the modeled inverter ⁇ inv,i was modeled as a 6th degree polynomial fit of a commercially available solar inverter (Power-One PVI-5000), scaled from a nominal 5 kW PV array of commercially available solar PV panels (Lumos LS250) to a per m 2 of array.
- the value of solar photovoltaic electricity energy and power produced by the photovoltaic arrays is calculated for the various placements using the estimated AC solar photovoltaic electricity energy and production, weather data and local market conditions or local utility rates.
- the value of energy production can correspond to maximizing or optimizing energy, power, economic value or non-economic value (e.g., carbon dioxide displacement).
- the value of maximizing energy production is dependent upon the user in question (e.g., resident in a residential area, a utility company, a business). That is, the value of maximizing energy production is dependent upon the user who is to benefit from the analysis discussed herein and might differ for different users.
- a second model was developed to calculate the solar PV electricity produced from a solar PV system for any given placement, accommodating different tilts and azimuths.
- This model consisted of three steps. First, given a placement and the horizontal solar radiation values, it calculated the solar radiation on a plane. Second, using the solar PV model discussed above and weather data, it calculated the energy produced at that placement. The last step calculated the value of the energy produced using either local market conditions or local utility rates.
- Price 1,i is the economic price (ERCOT SPP or TOU rate, $/kWh)
- Price 2,i is the price associated with reduction in overall demand charges for a commercial or industrial consumer that has the solar PV system behind the meter, all at time i.
- Price 2,i could also be used to estimate ancillary service value or a capacity payment.
- Price 2,i was considered to be fixed at 0 (because Texas has an energy-only market), but it could be considered in another analysis that looked at markets with capacity payments or the ability of solar PV to reduce demand changes for arrays behind the meter (many commercial and industrial customers have demand changes in addition to energy charges).
- this price could be considered on a case by case basis. This calculation was then completed for multiple radiation inputs (measured, Typical Meteorological Year (TMY), and clear-sky), weather inputs (measured and TMY), and pricing inputs (market and electric rate) for Austin.
- TMY Typical Meteorological Year
- TMY Typical Meteorological Year
- TMY clear-sky
- weather inputs measured and TMY
- pricing inputs market and electric rate
- the optimization used a quasi-Newton method (L-BFGS-B), a version of the Broyden-Fletcher-Goldfarb-Shanno algorithm with box constraints (Nocedal et al., Numerical Optimization, 2 nd Edition, New York: Springer, 2006, which is incorporated herein by reference in its entirety).
- the initial starting point was taken to be the local location's rule of thumb placement.
- the expanded model considered total energy produced, power produced, and the value of the produced energy.
- the energy-only model is the same as for the more Austin-specific analysis. However, the value of the energy model was somewhat different.
- local TOU energy rates were used as a proxy for the temporal value of energy, as it was assumed that these rates would be designed such that times of higher costs would be typically associated with times of higher grid stress/demand.
- step 204 the placement out of the various placements with the highest value of the solar photovoltaic electricity energy and power produced by the photovoltaic arrays is selected.
- the placement corresponding to the highest value of solar energy produced corresponds to the placement that optimally maximizes energy production based on placement, peak power production, local solar radiation, weather, electricity market prices and rate structures.
- the appropriate placement for the photovoltaic arrays is determined that maximizes the value of energy production (where “value” may correspond to an economic value or a non-economic value).
- the last step of the analysis was to explore the effects of solar placement on summer peak power reduction.
- the summer peak times are defined as June-August, from 14:00-20:00 CST for Austin, Tex. These times are typically associated with high wholesale electricity prices and grid stress, mainly due to residential air-conditioning load.
- Equation 10 the same approach was taken as with Equation 10, except the Price 1,i was given a value of 1 during summer peak hours and 0 otherwise.
- FIG. 3 is a table (Table 1) that summarizes the results of the various cases for both total energy production and the value of the energy produced in Austin, Tex. in accordance with an embodiment of the present invention.
- Table 1 summarizes the results of the various cases for both total energy production and the value of the energy produced in Austin, Tex. in accordance with an embodiment of the present invention.
- the TMY case shifts the arrays about 8° west of south.
- the cases shift the arrays about 20 to 51° west of south, depending on the price considered. While the increase in the amount of energy generated in the optimal cases was negligible, the increased economic values ($/m 2 /yr) for shifting the solar PV arrays west of south were on the order of 1-7%.
- FIG. 4 shows the total number of kWh per year produced (normalized for 1 m 2 of array) for every combination of azimuth and tilt, 90°-270° and 0°-45°, respectfully using clear-sky radiation and TMY weather data in accordance with an embodiment of the present invention.
- FIG. 4 is a heat map of model results for clear-sky radiation and TMY weather showing an optimal energy azimuth of 180° and 30° tilt. Contour lines show areas of percent of maximum energy in 5% increments.
- FIG. 5 shows the effect of using TMY radiation and weather on optimal placement in accordance with an embodiment of the present invention.
- FIG. 5 is a heat map of model results for TMY radiation and TMY weather showing an optimal energy azimuth of 188° and 28° tilt, indicating the due south azimuth might not be optimal for total energy generation in Austin, Tex. when typical meteorological conditions are considered.
- Contour lines show areas of percent of maximum energy in 5% increments. The number of kWhs overall are reduced compared to FIG. 4 because this data included the effects of clouds on the amount of solar radiation that reaches the earth's surface.
- FIGS. 6 and 7 show the optimal azimuth for the value ($/m 2 /year) of electricity produced (Equation 10) for the 2012-2013 measured data and coincident ERCOT prices and the TMY data with average ERCOT prices, respectfully, in accordance with an embodiment of the present invention.
- FIG. 6 is a heat map of model results for measured 2012-2013 radiation and weather with coincident ERCOT prices showing an optimal value ($/m 2 /year) azimuth of 204° and 25° tilt for Austin, Tex. Contour lines show areas of percent of maximum values in 5% increments.
- FIG. 7 is a heat map of model results for TMY radiation and weather with average ERCOT prices showing an optimal value ($/m 2 /year) azimuth of 219° and 29° tilt for Austin, Tex. Contour lines show areas of percent of maximum values in 5% increments.
- the placement is shifted west when optimizing based on market value.
- FIG. 8 shows the values associated with Austin TMY solar radiation and weather with the Austin Energy's residential TOU rate and also shows how azimuth and tilt are related under the TOU rate in accordance with an embodiment of the present invention.
- FIG. 8 is a heat map of model results for TMY radiation and weather with the Austin Energy's Residential TOU rate showing an optimal value ($/m 2 /year) azimuth of 200° and 25° tilt for Austin, Tex.
- Contour lines show areas of percent of maximum values in 5% increments. For example, if a solar PV array's azimuth were constrained to 150°, its optimal tilt is not the 25° associated with the unconstrained array, but 18°, a 0.5% ($/m2/year) difference.
- FIG. 9 shows the values associated with Austin TMY solar radiation and weather with ERCOT prices from 2011 in accordance with an embodiment of the present invention.
- FIG. 9 is a heat map of model results for TMY radiation and 2011 ERCOT prices showing an optimal value ($/m 2 /year) azimuth of 231° and 30° tilt for Austin, Tex. Contour lines show areas of percent of maximum values in 5% increments.
- a high price cap and more instances of scarcity pricing could have an impact on the optimal placements of fixed solar PV installations, namely further west with a steeper tilt. Utilities could incentivize these solar placements as a hedge towards a more volatile wholesale electricity market.
- FIG. 10 shows the results of the energy-only analysis.
- FIG. 10 is a map of continental U.S. showing the energetically optimal azimuth of solar PV systems in accordance with an embodiment of the present invention.
- Points 1001 indicate southerly optimal solar azimuths (160°-170°)
- points 1002 indicate southerly optimal solar azimuths (170°-190°)
- points 1003 indicate southerly optimal solar azimuths (190°-200°)
- points 1004 indicate optimal azimuths west of south (greater than 200°).
- FIG. 11 shows the results when considering the maximum economic value of the solar energy produced for all considered solar placements.
- FIG. 11 is a map of continental U.S. showing the optimal azimuth of solar PV systems when considering the value of the solar energy produced in accordance with an embodiment of the present invention.
- Points 1101 indicate southerly optimal solar azimuths (160°-170°)
- points 1102 indicate southerly optimal solar azimuths (170°-190°)
- points 1103 indicate southerly optimal solar azimuths (190°-200°)
- points 1104 indicate optimal azimuths west of south (greater than 200°).
- the value of the electricity produced is approximated by the structure of a utility TOU pricing structure that is either in the state of the TMY data location, or if the state does not have a TOU rate available, the closest location with a TOU rate was chosen.
- FIG. 12 shows the deviation from the rule of thumb (i.e. local latitude) for optimal energetic tilt in each location.
- FIG. 12 is a map of continental U.S. showing deviation from the rule of thumb tilt (local latitude) based on total energy production in accordance with an embodiment of the present invention. Negative values means that the optimal tilt is below the local latitude.
- FIG. 12 suggests that while accurate for parts of the southwest U.S., the optimal energy tilt is typically lower than the local latitude, especially in the states surrounding Tennessee and Kentucky. Lower optimal tilts would indicate the prevalence of more sunny days when the sun is higher in the summer sky.
- FIG. 13 shows a map of the deviation from the rule of thumb tilts as determined by the maximum value ($/m 2 /year based on local TOU electric rates) of the solar energy produced.
- FIG. 13 is a map of continental U.S. showing deviation from the rule of thumb tilt (local latitude) based on the value of local energy production in accordance with an embodiment of the present invention. Negative values means that the optimal tilt is below the local latitude.
- FIGS. 12 and 13 are very similar, except in situations where the local rates incentivize either more summer or winter production. For example, in California, high summer afternoon electricity prices force the optimal tilt lower to produce more during the summer peak.
- FIGS. 14A-14B are plots that show the average generation curves for various solar placements in Austin using TMY data, including optimal peak placement in accordance with an embodiment of the present invention.
- FIG. 14A shows the generation curves for the entire year and FIG. 14B shows the curves for only the summer months (June-August).
- FIG. 15 is a table (Table 2) that summarizes the differences in energy produced (area under the curves) from the placements shown in FIGS. 14A-14B in accordance with an embodiment of the present invention.
- Table 2 illustrates the percent change in the amount of energy generated by various solar PV placements as compared to a south facing) (180°/30° array for an entire year, only the summer months (July-August), and for just the peak hours during the summer months (14:00-20:00) for Austin, Tex.
- the optimal energy and optimal value placements do not differ much from south placements in terms of energy use.
- west facing and optimal peak placement generate about 14 and 20% less energy throughout the year.
- the optimal energy, optimal value, and the west-facing array generate about the same amount of energy as the south facing array with the optimal peak array generating less.
- all placements generate more energy than south-facing arrays with west and optimal peak placements generate 23 and 24% more energy during peak hours, respectfully.
- TMY data indicate an 8° shift west (188°) and a few degrees towards the horizontal (from the rule-of-thumb 30°) might be a better azimuth and tilt for energy production.
- Clear sky radiation data reinforce the energy rule-of-thumb as expected.
- the optimal azimuth was pushed further west (approximately 20-51°) based on wholesale electricity market prices that are typically higher in the mid to late afternoon hours. While the resulting improvements might seem small, ( ⁇ 1-7% difference), the improvement could be free to implement during construction, and over the 25 year lifespan the excess energy produced and revenue earned could be significant.
Abstract
Description
I T =B T +R T +D T (1)
B T =I B R B (2)
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CN108664500B (en) * | 2017-03-30 | 2021-06-29 | 中国电力科学研究院有限公司 | Grid management method and system for distributed photovoltaic |
US11022699B1 (en) * | 2017-11-22 | 2021-06-01 | Cory A. Webb | External solar power source for global positioning system (GPS) base stations |
CN111209520A (en) * | 2020-01-17 | 2020-05-29 | 中国电力科学研究院有限公司 | Method and system for calculating output power of photovoltaic array |
CN111815021A (en) * | 2020-06-04 | 2020-10-23 | 上海电力大学 | Photovoltaic power prediction method based on solar radiation climate characteristic identification |
CN115423200B (en) * | 2022-09-16 | 2023-12-29 | 南通沃太新能源有限公司 | Method for predicting photovoltaic power by supplementing solar irradiation in off-line state |
CN115983011B (en) * | 2023-01-04 | 2024-03-22 | 四川省建筑设计研究院有限公司 | Photovoltaic power generation power simulation method, system and storage medium based on annual radiation quantity |
CN116086394A (en) * | 2023-04-10 | 2023-05-09 | 中国气象局公共气象服务中心(国家预警信息发布中心) | Method and device for determining azimuth angle of photovoltaic array based on asymmetric radiation distribution |
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